Reverse Exchangeable Securities

8/3/2019 Reverse Exchangeable Securities

http://slidepdf.com/reader/full/reverse-exchangeable-securities 1/44

An Economic Analysis of Reverse Exchangeable Securities

— An Option-Pricing Approach

By

Rodrigo Hernández*

Wayne Y. Lee **

Pu Liu***

May 21, 2007

JEL classification: G13, G24

Keywords: Reverse Convertible; Discount Certificate; Knock-In; Knock-Out;Option Pricing; Structured Products

* Department of Finance, Sam M. Walton College of Business, University of Arkansas,Fayetteville, Arkansas 72701. E-mail: [email protected] (479) 575-3101

** Alice Walton Professor of Finance, Department of Finance, Sam M. Walton College of Business, University of Arkansas, Fayetteville, Arkansas 72701. E-mail: [email protected] (479) 575-4505

*** Corresponding author. Harold A. Dulan Professor of Capital Formation and Robert E,Kennedy Professor in Finance, Department of Finance, Sam M. Walton College of Business,University of Arkansas, Fayetteville, Arkansas 72701. E-mail: [email protected] (479) 575-6095

We are thankful to Basilio Lukis, Jeremie Magne, Sergio Santamaria, Michael Villines, andAlfonso Vrsalo for their assistance in the data collection, seminar participants at The Universityof Melbourne, University of Arkansas, and 2007 FMA European Doctoral Student Seminar for their comments, and the financial support provided by the Bank of America Research Fundhonoring James H. Penick and the Robert E. Kennedy Professorship Foundation. Remainingerrors, if any, are solely ours. This is a preliminary draft. Comments are welcome. Do not citewithout the authors' permission.





Abstract

In this paper we provide economic and empirical analyses for reverse exchangeable

bonds. We make a detailed survey of the $ 45 billion US dollar-denominated market for

7,426 issues of bonds issued between May 1998 and February 2007. In addition, we also

develop pricing models for four types of bonds and empirically examine the profits for

issuing these bonds. The results of the survey suggest significant positive profits for the

issuing financial institutions. We also show that a perfect hedge can be obtained through

static and costless trading strategies and find that issuing reverse exchangeables with the

perfect hedging strategy has a payoff identical to the payoff of a call option.



3



I. Introduction:

The development of structured products -- that is to create new securities through the

combination of fixed income securities, equities and derivative securities -- has been rapidly

accelerating for more than one decade. The creation, underwriting and trading of structured products

have become a significant source of revenues for many investment and commercial banks.

The development of structured products is part of the financial innovation process that

provides important functions in the financial market. For instance, the structured products enhanced

the capital market efficiency by combining the transactions of several securities into one and thus

reduced transaction costs. The development of structured products has also challenged practitioners,

academicians, and regulators. For instance, some structured products may include exotic derivatives

that are difficult to price and regulators are concerned that some structured products may be too

complicated for unsophisticated investors to understand.1

However, the complication of the products

and regulators’ concerns of investors’ inability to understand the risk have not slowed down the

development and marketing of such products. Instead, the trend in the market is the design of more

complicated structured products (e.g. moving from standard options to exotic options) and targeting

individual investors as primary customers.

In this paper, we introduce a product known as “reverse exchangeable bond” to examine how

the product is structured. We especially examine how plan vanilla standard options were replaced

1 For instance, the National Association of Securities Dealers expressed its concerns of unsophisticated investors’investment in structured products in its publication Notice to Members 05-59 entitled “Guidance Concerning the Sale of Structured Products” (September 2005).



4

by more complicated exotic options in the design of the products. We provide detailed descriptions

and analyses of the market for the $45 billion US dollar-denominated reverse exchangeable bonds

issued between May 1998 and February 2007. We also examine whether and how the issuers make

a profit in the primary market and how issuers can perfectly hedge the risk for issuing such bonds.

Several studies (e.g. Benet, Giannetti, and Pissaris (2006), Burth, Kraus, and Wohlwend

(2001), Grünbichler and Wohlwend (2004), Stoimenov and Wilkens (2005), Szymanowska, Horst,

and Veld (2004), Wilkens, Erner, and Roder (2003)) have consistently reported that these bonds

were overpriced based on theoretical pricing models. In this paper, we extend the previous studies to

US dollar-denominated securities making an extensive survey of its market.

The rest of the paper is organized as follows: we introduce the structure of the products in

Section II. We then provide detailed analyses of the $45 billion US dollar-denominated reverse

exchangeable bond market which includes 7,426 bonds issued between May 1998 and February

2007 (Section III). We further analyze these structured products and show how these reverse

exchangeable bonds can be decomposed into zero coupon bonds and short positions in put options

on the underlying assets (Section IV). Furthermore, we price 6,515 issues of the reverse

exchangeable bonds that have complete data based on the valuation models developed in the paper

and analyze the profitability of these bond issues. We find that on average issuers make a profit of

3%-6% in the $45 billion market (Section V). We further show that the hedging strategy for plain

vanilla bonds and discount certificates can be perfect (i.e. complete risk-free) and costless.

Moreover, we find that the prefect and costless hedging can be reached through one-time purchase of

the underlying asset (i.e. no dynamic hedging is needed). These results are presented in Section VI

of the paper. We further explore how the underlying assets of the securities are selected in Section





6

⎪⎩

⎪⎨

⎧

<

≥

=0T

0

T

0T

T II if I

$1,000I

II if $1,000

V …(1)

Alternatively, the relationship between the redemption value on a reverse exchangeable bond

and the valuation price of the underlying asset can be represented in Figure 1.

Figure 1: The terminal value of a Reverse Exchangeable Bond, VT, as a function of the valuation price of the underlying asset, IT.

There are at least two differences between a convertible bond and a reverse exchangeable

bond. First, in the case of a convertible bond, it is the owner of the bond that has the right to

convert the bond into the underlying assets. In a case of a reverse exchangeable bond, however,

it is the issuer of the bond that has the right to deliver the underlying asset to the investors, and

that is why the term “reverse” is used in the security. Secondly, for a convertible bond, the

underlying stock that the bond investors have the right to convert to is issued by the same firm

that issues the bonds. For a reverse exchangeable bond, however, the issuer of the underlying

$1,000

Slope = 1

Terminal Value VT

I0 = X IT



7

asset is virtually always different from the issuer of the bond. This is why the term

“exchangeable” is used.3

When investors purchase a reverse exchangeable bond they basically engage in two

transactions simultaneously: they take a long position in a typical fixed-rate bond and they short

several contracts of put options. The underlying asset of the put option is the underlying asset of

the reverse exchangeable, the exercise price of the put option is the initial price of the underlying

asset, the expiration date of the put option is the maturity date of the reverse exchangeable, and

the number of contracts written is the face value of the reverse exchangeable bond (usually

$1,000) divided by the initial price of the underlying asset. The bond issuer will exercise the

option by delivering the underlying asset to the bond investor when the underlying asset price on

the maturity date of the bond is lower than the exercise price. The high coupon payments made

by the reverse exchangeable basically include the option premium paid by the bond issuer to the

investors of the reverse exchangeable bonds.

In addition to the plain vanilla reverse exchangeables, there are three other types of reverse

exchangeables, they are discount certificates, knock-in reverse exchangeables , and knock-out

reverse exchangeables. We will introduce each of them briefly as follows:

B. Discount Certificate:

A discount certificate is a special case of a plain vanilla reverse exchangeable in that a

discount certificate does not make coupon payments. A discount certificate, therefore, can be

viewed and priced as a plain vanilla reverse exchangeable bond with a coupon rate equal to zero.

3 Most “reverse exchangeable” issuers, however, use the incorrect term “reverse convertible” when they really mean“reverse exchangeable” because the underlying assets that they have the right to deliver to investors are the stocks issued by other companies, rather than of their own. In the paper, we will use the correct term “reverse exchangeable” for such bonds.



8

C. Knock-In Reverse Exchangeable Bond:

A knock-in reverse exchangeable bond is similar to a plain vanilla reverse exchangeable

except that in a knock-in reverse exchangeable the bond issuer has the right to exercise the option

of delivering the underlying asset to bond investors only if the underlying asset price has dropped

to a predetermined level (which is usually set below the initial price) anytime between the issue

date and the maturity date of the bond. The predetermined level of the underlying asset price is

referred to as the knock-in level (or limit price).4 Since the knock-in level is generally set below

the initial price, the bonds are also referred to as “down-and-in” reverse exchangeables. On the

maturity date of the bond (t=T), for each bond the issuer will pay to investors the par ($1,000) or

deliver to the investor the shares of the underlying security (known as the redemption amount )

according to the following conditions:

⎪

⎪⎪

⎩

⎪⎪⎪

⎨

⎧

∈≤<

∈><

≥

=

T][0,tH,IsomeandII if II

$1,000

T][0,tH,IallandII if $1,000

II if $1,000

V

t0TT0

t0T

0T

T…(2)

Where ],0[ T t ∈ is the time between the issue date of the bond and the maturity date of the

bond. The H in Equation (2) is the pre-specified knock-in level.

D. Knock-Out Reverse Exchangeable Bond:

A knock-out reverse exchangeable bond is similar to a plain vanilla reverse exchangeable

except that in a knock-out reverse exchangeable the bond issuer loses the option of delivering the

underlying asset to the investors if the underlying asset price moves above a predetermined level

(which is usually set above the initial price) anytime between the issue date and the maturity date

4 Usually the knock-in level is set up as a percentage of the initial price (e.g. 70% of the initial price). A bond with aknock-in level of, for example, 70% of the initial price, is also referred to as having a 30% downside protection.



9

of the bond. The predetermined level of the underlying asset price is referred to as the knock-out

level (sometimes also referred to as limit price). Since the knock-out level is set above the initial

price, the bonds are also referred as “up-and-out” reverse exchangeables.5

The redemption amount of a knock-out reverse exchangeable bond on maturity date T is

given as

⎪

⎪⎪

⎩

⎪⎪⎪

⎨

⎧

∈<<

∈≥<

≥

=

T][0,tH,IallandII if II

$1,000

T][0,tH,IsomeandII if $1,000

II if $1,000

V

t0TT0

t0T

0T

T…(3)

Where H is the pre-specified knock-out level.

In Appendixes 1 and 2, we present the summary information for two reverse exchangeable

bonds in our sample: one plain vanilla reverse exchangeable bond and one knock-in reverse

exchangeable bond respectively.

III. The Reverse Exchangeable Bond Market:

In Table 1 we present the descriptive statistics for the four types of the products: plain

vanilla, the discount certificate, the knock-in, and the knock-out r everse exchangeable bond

markets. The total value issued is $6.7 billion on 665 issues of plain vanilla bonds; $9.9 billion

on 2,016 issues of discount certificates; $28.0 billion on 4,662 issues of knock-in bonds; and

$0.4 billion on 83 issues of the knock-out bonds. Thecombined value of reverse exchangeable

bonds is about $45 billion on 7,426 issues. The median term to maturity is close to one year for

all types except for discount certificates that have a median term to maturity of 59 days. The

5 Usually the knock-out level is set up as a percentage of the initial price (e.g. 120% of the initial price).



10

median issue size ranges from $2 million to $5 million and the median coupon rate ranges from

9% to 12% for the interest bearing types. The median barriers are set at 80% and 120% of the

strike price for the knock-in bonds and knock-out bonds respectively.

In Table 2 we break down the statistics for the reverse exchangeable bond markets by the

issue year and the type. The combined reverse exchangeable bond market consists of 7,426

bonds issued between May 1998 and February 2007. One phenomenon especially worth noting

is that the market is growing extremely rapidly. In terms of numbers of new issues, the

compounded annual growth was at an amazing rate of 75% over the last seven years (from 70

issues in 1999 to 3,537 issues in 2006). The compounded annual growth was even higher at an

astonishing rate of 136% over the last two years (from 633 issues in 2004 to 3,537 issues in

2006). In terms of dollar amount, the growth was equally impressive. The compounded annual

growth was an amazing rate of 40% over the last seven years (from $1,715 million in 1999 to

$18,526 million in 2006), and it was even higher over the last two years at an astonishing rate of

113% (from $4,066 million in 2004 to $18,526 million in 2006). In addition, the composition of

the bond types also migrates over time from bonds featured with plain vanilla options to bonds

characterized with exotic options. For instance, the percentage of plain vanilla bonds and

discount certificates decreases from 90% of the total issues in 1999 to less than 20% in 2006.

On the other hand, the percentage of knock-ins increases from 10% of the total issues to 80% to

the total issues during the same period.

In Table 3 we further break down the number of issues and dollar amount by the countries in

which the issuing banks are located and by year. It is apparent that Netherlands and Great

Britain dominate the reverse exchangeable bond market, followed by Germany and the United

States. Out of a total of 7,426 issues of reverse exchangeable bonds (for a total value of $45



11

billion), 2,931 issues (for a total value of $11.3 billion) were issued in Netherlands, 1,906 issues

for a total of value of $17.9 billion) were issued in Great Britain, 1,117 issues (for a total value of

$5.6 billion) were issued in the United States, and 879 issues (for a total value of $7.5 billion)

were issued in Germany. During the earlier years, the market was dominated by banks or

branches of banks located in Great Britain (Barclays, UBS, Goldman Sachs, Credit Suisse Bank,

Credit Lyon, etc), and in Netherlands (ABN-AMRO, ING, RaboBank, etc). However, banks

located in the US are catching up recently. The banks or branches of banks in the US issuing

reverse exchangeable bonds include Societe Generale, Wachovia, Morgan Stanley, Merrill

Lynch, Lehman Brothers, JP Morgan, and Bear Stearns. Their market shares represent about

20% of the market in terms of dollar amount as well as in number of issues. Although not

reported in Table 3, our data indicates the top 5 banks measured by total number of issues

between 1999 and February 2007 are: ABN-AMRO (31%), Commerzbank (10%), Barclays

(9%), Societe Generale (8%), and Credit Lyon (6%).

We also classify the issues by the industries of the underlying securities based on the two-

digit SIC codes and the results of the classification are reported in Appendix 3. As shown in the

Appendix, the two industries in which the securities are most frequently used as underlying

securities are Electronic and Other Electrical Equipment and Components (SIC code 36), and

Industrial and Commercial Machinery and Computer Equipment (SIC code 35). Of the 7,426

issues reverse exchangeable bonds in the sample, 17% (1,244 issues) have underlying securities

in the industry of Electronic and Other Electrical Equipment and Components (SIC code 36), and

14% (1,017 issues) have underlying securities in the industry of Industrial and Commercial

Machinery and Computer Equipment (SIC code 35).



12

IV. The Pricing of Reverse Exchangeable Bonds:

A. Plain Vanilla Reverse Exchangeable Bond:

In this section we will develop the pricing model for plain vanilla reverse exchangeable

bonds. Assume the face value is $1,000, the coupon payments are C per time period, and the

selling price of the bond is B0. As we show in Appendix 4 of the paper, the payoff for an initial

investment in one plain vanilla reverse exchangeable bond with a strike price of I0, and a term to

maturity T, is exactly the same as the payoff for holding the following three positions:

1. A long position in one zero coupon bond with face value equal to $1,000 and maturity

date same as the maturity date of the reverse exchangeable;

2. A long position in zero coupon bonds of which the face values equal the coupons

payments of the reverse exchangeable and maturity dates are the reverse

exchangeable coupon payment dates;

3. A short position in put options with exercise price of I0, term to expiration of T

(which is the term to maturity of the reverse exchangeable), and number of options of

0I

000,1$.

Since the payoff of a plain vanilla reverse exchangeable bond is the same as the combined

payoffs of the above three positions, we can price the fair value of the reverse exchangeable

based on the three positions. Any selling price of the bonds above the value of the three

positions is the gain to the bond issuer.

The value of Position 1 is the price of a zero coupon bond with a face value $1,000 and

maturity date T. So it has a value of T r e 000,1$ − . The value of Position 2 is the present value of



13

the coupon payments of the reverse exchangeable bond, ∑ −n

i

t r iCe . The value of Position 3 is

the value of 0I

000,1$shares of put options with each option having the value P6:

) N(-d e) N(-d eP qT rT

1020 II −− −= …(4)

Where r is the risk-free rate of interest, q is the dividend yield of the underlying assets, T is

the term to maturity of the reverse exchangeable bond, X (≡ I0) is the exercise price7

and

T

T qr I

I

d σ

σ ⎟ ⎠

⎞⎜⎝

⎛ +−+⎟⎟

⎠

⎞⎜⎜⎝

⎛

=

2

0

0

1

2

1ln

T

T qr

σ

σ ⎟ ⎠ ⎞⎜

⎝ ⎛ +−

=

2

21

T d d σ −= 12

Where σ is the standard deviation of the underlying asset return. Therefore, the profit

function, ∏ for the issuing firm is:

T

n

i

t r V Ce B i −=∏ ∑ −

0 -

PeCe B T r n

i

t r i

0

0I

000,1$000,1$- +−= −−∑ …(5)

[ ]) N(-d e) N(-d eeCe B T qrT T r n

i

t r i

1

020

0

0 III

000,1$000,1$- −−−− −+−= ∑

[ ]) N(-d e) N(-d eeeC B qT rT rT n

i

t r

ii

12

0 000,1$000,1$ −−−− −+−−= ∑ …(6)

6 The pricing formula for this put option is a special case of the Black-Scholes general model for a put in that the exercise price, X, is the same as the initial stock price (i.e. X = I0).

7 Theoretically, the exercise price X should be the same as I0, the price of the underlying asset on the issue date. For most cases this is true, but there are exceptions. For instance, in some cases the underlying assets prices on the day (or afew days) before or after the issue date are used as exercise prices. In some cases the rounded underlying assets priceson the issue date are used as the exercise prices. In the empirical data, we use the actual exercise prices taken from thefinal term sheets.



14

It is also worth noting that, although the initial price I0 is explicitly specified in the contract

of reverse exchangeable bonds, I0 vanishes both in Equation (6) and in d1 and d2. The fact that

the profit function for issuing reverse exchangeables independent of the initial price I0 is a very

important feature in the design of a reverse exchangeable because once a reverse exchangeable

bond is designed, it can be issued any time before maturity regardless the price of the underlying

stock since the issuer’s profit will not be affected by the price.

B. Discount Certificate:

As we show in Appendix 5 of the paper, a discount certificate is a special case of plain

vanilla reverse exchangeable in which the bond is a zero coupon bond and the number of

embedded put options is one. The profit function ∏ for the issuer of a discount certificate,

therefore, is a reduced form of Equation (5).8

T V B −=∏ 0

P X

e B T r 000,1$000,1$

0 +−= − …(7)

where

) N(-d e) N(-d XeP qT rT 102 I −− −= …(8)

and

T

T qr X

I

d σ

σ ⎟ ⎠

⎞⎜⎝

⎛ +−+⎟

⎠

⎞⎜⎝

⎛

=

20

1

2

1ln

T d d σ −= 12

C. Knock-In Reverse Exchangeable Bond:

The profit function ∏ for the issuer of a knock-in reverse exchangeable, therefore, is a

modified form of Equation (5) where the short positions the put options are down-and-in puts

8 To use a general notation to cover all possible cases for the exercise price, we use X.



15

instead of standard puts. Based on Hull (2003), when the knock-in level is lower than the strike

price, the price for a down-and-in put, Pdi, can be express as:

( ) ( ) [ ]

( ) ( )[ ]T y N T y N H

Xe

y N y N

H

eT x N Xe x N eP

rT

qT rT qT

di

σ σ

σ

λ

λ

−−−⎟⎟ ⎠

⎞⎜⎜⎝

⎛ −

−⎟⎟ ⎠

⎞

⎜⎜⎝

⎛ ++−+−−=

−

−

−−−

1

22

0

1

2

00110

I

)()(III…(9)

Where r is the risk-free rate of interest, q is the dividend yield of the underlying stock, T is

the expiration date of the put option, X is the exercise price of the put option 9, I0 is the

underlying asset initial price, σ is the standard deviation of the underlying asset return, H is the

knock-in level, and

T T

H x λσ

σ +

⎟ ⎠

⎞⎜⎝

⎛

=

0

1

Iln

T T

H

y λσ σ

+⎟⎟ ⎠

⎞⎜⎜⎝

⎛

= 0

1

Iln

T T

X

H

y λσ σ

+⎟⎟ ⎠

⎞⎜⎜⎝

⎛

= 0

2

Iln

( )2

2

2σ

σ

λ

+−=

qr

The profit function of the issuer of the bond at the issue date t=0 is

dirT n

i

t r

i PeeC B i

0

0I

000,1$ 000,1$ +−−=∏ −−∑ …(10)

9 For knock-in reverse exchangeables, the exercise price is the same as the initial stock price (i.e. X=I0 ).





17

V. The Hedging Strategies:

One important and interesting question for the issuers of plain vanilla reverse exchangeables

(and discount certificates) is if and how the issuer can perfectly hedge the risk. We will show

that the issuer can perfectly hedge the risk by purchasing 1,000/ I0 shares of the underlying asset

on the issue date at the price I0 for each bond to be issued.

Since the only uncertain cash flow faced by the bond issuer is the redemption value, -VT (all

other cash flows are known at t=0), all we need to show is how the uncertainty in cash flow –VT

can be completely eliminated when the issuers purchase $1,000/ I0 shares of underlying assets

for each bond they issue.

After the purchase of $1,000/ I0 shares of the underlying asset, the combined value of the

purchased underlying assets and the contingent payment of the reverse exchangeable bond on

maturity date T, FT, will be

T T V ,$

F −⎟⎟ ⎠

⎞⎜⎜⎝

⎛ = T

0

II

0001 …(14)

Substitute the value of VT in Equation (1) into Equation (14), we obtain

⎩⎨⎧

<

≥−×=

⎪⎩

⎪⎨

⎧

<

≥−=

0T

0T0T

0

0T

0TT

0

II0

II)II(

I

000,1$

II0$

II000,1$II

000,1$

if

if

if

if F T

]II,0[I000,1$

0T

0

−= Max …(15)

Equation (15) is non-negative. Therefore, the total value of the contingent payment of the

reverse exchangeable, -VT, combined with the long position in the underlying asset, 1,000IT/I0,





19

The fourth feature of the hedge is that the static and perfect hedge is also costless. In other

words, the profit function for the firm issuing reverse exchangeable bonds will not be affected by

the hedging position taken by the firms. To prove this argument, we will calculate the profit

function for a firm taking the hedging position and show that the profit function is identical to

Equation (6) –the profit function for a firm not taking any hedging position.

The [ ]0T II,0Max − in Equation (15) is the payoff for a long position in a call with an

exercise price of I0. The present value of the payoff [ ]0T II,0Max − , based on Black-Scholes

model, is11

)(I)(I 2010 d N ed N eCall rT qT −− −= …(16)

Where

T d d T

T qr

T

T qr I

I

d

σ σ

σ

σ

σ

−=

+−=

+−+⎟⎟ ⎠

⎞⎜⎜⎝

⎛

=

12

2

2

0

0

1

)2

1(

)2

1(ln

The cash flows for a firm taking the hedging position can be depicted as Figure 2:

t=0 t1 t2 t3 … T

+B0 -(1,000/I0)I0 -C1 -C2 -C3 … -CT +FT

= B0-$1,000

Figure 2: The cash flows for a reverse exchangeable issuer after hedging the risk of uncertaincash flows on maturity date T by taking a long position in the underlying asset on the bondissue date t=0, where FT is the cash flow characterized by Equation (15).

11 The pricing formula for this call is a special case of the Black-Scholes general model for a call in that the exercise price, X, is the same as the initial stock price (i.e., X=I0).



20

The profit function based on the cash flows displayed in Figure 2 for the issuing firm at t = 0 is:

∑ +−⎟⎟ ⎠

⎞⎜⎜⎝

⎛ −=Π −n

i T

rt

i F PV eC B i )(II

000,1$0

0

0'

[ ]

[ ]

[ ] [ ]{ }1)(1)(000,1$000,1$

)()(000,1$000,1$

)(I)(II

000,1$000,1$

210

210

2010

0

0

−−−+−−=

−+−−=

−+−−=

−−−

−−

−−

∑

∑

∑

d N ed N eeC B

d N ed N eC B

d N ed N eC B

rT n

i

rT rt

i

rT n

i

rt

i

rT n

i

rt

i

i

i

i

Since

1-N(d1) = N(-d1)

1-N(d2) = N(-d2)

'

0 1 2$1,000 $1,000 ( ) ( )in rt rT rT

ii B C e e N d e N d − − −⎡ ⎤Π = − − + − − + −⎣ ⎦∑ …(17)

The profit function for an issuing firm taking the hedging position, ∏', in Equation (17) is

identical to the profit function for an issuing firm that does not take any hedging position.

Therefore, we conclude that the hedging of taking a long position in the underlying asset of a

reverse exchangeable bond at t = 0 is not only perfect , static (i.e., it requires no subsequent

rebalancing or any other transactions), but also costless.

VI. The Profitability of Reverse Exchangeable Bonds:

In this section, we examine the profits for issuing reverse exchangeables. First, we calculate

the profit for each issue of bond that has complete data based on Equation (6) (for plain vanilla

reverse exchangeables), Equation (7) (for discount certificates), Equation (10) (for knock-in

reverse exchangeables), and Equation (13) (for knock-out reverse exchangeables) respectively.

We then classify the bonds 1) by issue year , 2) by term to maturity, and 3) by country in which

the bonds are issued. We find that issuing bonds is profitable for virtually all four types of



21

bonds, by all issue years, across all the maturities of the certificates, and among all the countries

in which the certificates are issued.

A. Data Description:

In order to calculate the profit, we need the following data for each bond: 1) the bond price

(B0), 2) the coupons (C) and the coupons payment dates, 3) the price of the underlying asset (I 0),

4) the cash dividends of the underlying assets and the ex-dividend dates so we can calculate the

dividend yield, q12, 5) the risk-free rate of interest, r, 6) the exercise price (X) of the options

component in the certificate, 7) the volatility (σ) of the underlying asset, and 8) the term of

maturity of the bond (which is also the term to expiration of the option included in the

certificate), T.

The bond prices, B0, are obtained from the final term sheets published on the web pages of

issuing banks. We double check the prices and other variables in the Bloomberg Information

System and several websites to ensure the accuracy of the data.13

The prices of underlying

assets are obtained from the Bloomberg System; dividend data are taken from I/B/E/S on the

Bloomberg; the risk-free rates of interest are the yields on government bonds with the same

maturities as the certificates. 14 The exercise prices (X) of the options, the coupons (C) paid by

the bonds, the coupon payment dates (t), and the terms to maturity of the certificates (T) are all

12 The profits in equations (6), (7), (10), and (13) are based on continuous dividend yield. Since dividends for individualstocks are discrete, we calculate the equivalent continuous dividend yield for stocks that pay discrete dividends. SeeAppendix 6 for the details of how equivalent continuous dividend yield is calculated from discrete dividends.

13

These websites include OnVista (Germany www.onvista.de), the Yahoo (Germany http://de.yahoo.com),ZertifikateWeb (Germany www.zertifikateweb.de), TradeJet (www.tradejet.ch), Berlim-Bremen Boerse Stock Exchange(www.berlinerboerse.de), Stuttgart Boerse Stock Exchange (www.boerse-stuttgart.de), American Stock and OptionsExchange (www.amex.com), U.S. Securities and Exchange Commission (www.sec.gov), and Swiss Stock Exchange(www.swx.com).

14 We match the maturity dates of government bonds with those of the certificates. When we cannot find a government bond that matches the term of maturity for a particular certificate, we use the linear interpolation of the yields from twogovernment bonds that have the closest maturity dates surrounding that of the certificate.



22

taken from the final term sheets. The volatilities (σ) of the underlying assets are the implied

volatilities obtained from the Bloomberg Information System based on the put options of the

underlying asset.15

For a few cases when the implied volatility is not available, we use the

historical volatility calculated from the underlying securities prices in the previous 260 days.

B. Empirical Results of the Profitability Analysis:

In Table 4, we present the profitability for issuing reverse exchangeable by security type.

The profitability is measured by the profit (∏) as a percentage of the total issuing cost (TC), i.e.

Profitability = %100*TC

Π

%100*TC

TCB0 −

= … (18)

The results in Table 4 show that the reverse exchangeable issuers made statistically

significant profits in the markets. The average profit for the 6,515 issues in the sample is a hefty

4.69% above the issuing cost. With a total market value of $45 billion, the profitability measures

translate into a profit of $2.11 billion.

The profits for issuing the certificates are consistent no matter how we break down the data.

We break down the profit by issue year (Table 5), by terms to maturity and by countries in

which the bonds are issued in (Table 6). The results in these tables consistently indicate that the

profits of issuing the bonds are statistically significantly positive. The results in Tables 4-6

suggest that issuing reverse exchangeables is a profitable business.

15 The implied volatility calculated by the Bloomberg System is the weighted average of the implied volatilities for thethree put options that have the closest at-the-money strike prices. The weights assigned to each implied volatility arelinearly proportional to the “degree of near-the-moneyness” (i.e. the difference between the underlying asset price andthe strike price) with the options which are closer-to-the-money receive more weight.



23

VII. The Selection of Underlying Assets:

In this section, we explore how underlying assets are selected. Our conjecture is, in order to

enhance the marketability of the bonds, issuers are more likely to select securities highly

recognized in the market. Therefore, underlying securities tend to be the stocks of large firms.

In addition, stocks of large firms tend to be more liquid and their options may also be more

widely held and more frequently traded and the liquidity will make hedging easier and less

costly. Based on the hypothesis, we empirically examine the firm size of the underlying

securities and the results are reported in Panel A of Table 7. As shown in the panel, the average

market capitalization for the underlying assets ($26.1 billion) is significantly higher than the

average size of the firms in the same industry both at the country level ($9.1 billion) and at the

regional level ($6.5 billion). The average percentile ranking of the market capitalization for the

underlying assets among all the stocks in the same industry is 84.4% at the country level and

87.1% at the regional level. The results confirm our conjecture.

Along the same line on how certificate issuers select underlying securities, we hypothesize

that issuers have an incentive to use the level of dividend yield as one of the selection criteria for

underlying assets. Since a higher dividend yield will lead to a higher value of the put option, P,

Equation (6) suggests that a higher dividend yield implies a higher profit for reverse

exchangeable issuers. We hypothesize that issuers tend to select stocks with high dividend yield

as the underlying assets. To test the hypothesis, we compare the dividend yield of the underlying

assets with the average dividend yield for all the stocks in the same industry both at the country

level and at the regional level. We also calculate the percentile ranking of the dividend yield for

the underlying assets among all the stocks in the same industry at both the country and the

regional levels. We present the results in Panel B of Table 7. The average dividend yield for





25

exchangeable bonds issued between May 1998 and February 2007. In addition to the realized

return for each expired reverse exchangeable bond, we also calculate, for each bond, the total

return (price appreciation plus dividend) on the underlying asset as well as the total return on a

benchmark index16 over the same period as the term to maturity of the reverse exchangeable

bonds and present the results in Table 9.

As shown in Table 9, over the same period as the term to maturity of the bond, the average

return on the underlying assets is consistently higher than that of the benchmark index, with

higher standard deviation. For instance, for the combined sample of all four types of reverse

exchangeable bonds, the average return for the underlying assets is 33.90% (with a standard

deviation of 188.39%) while the average return for the benchmark index is 11.38% (with a

standard deviation of 31.28%). The results suggest that a typical underlying asset tend to have a

higher return (and also higher risk) that its benchmark index.

The results in Table 9 also indicate that the realized return on reverse exchangeable bonds

also tend to be lower than the return on underlying assets (and the index as well) with lower risk

than both the underlying assets and the indices. For instance, for all four types of reverse

exchangeable bonds, the average realized return is 2.87%, which is lower than the return on the

underlying asset (33.9%) and the index (11.38%), while the standard deviation for the reverse

exchangeable bond is 23.86%, which is also lower than the standard deviation for the underlying

assets (188.39%) and the benchmark indices (31.20%).

16 The benchmark index is the index representative of the large-capitalization stocks in the market of the underlyingsecurity. Whenever the underlying is an index, the benchmark index will be the index representative of market at thehigher level of aggregation.





27

REFERENCES

Baubonis, C., Gastineau, G.I., Purcell, D., 1993. The banker’s guide to equity-linked certificates of deposit. Journal of Derivatives 1 (Winter), 87--95.

Benet, B., Giannetti, A. and Pissaris, S., 2006. Gains from structured product markets: The case of reverse-exchangeable securities (RES). Journal of Banking and Finance 30, 111--132.

Black, F. and Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637--659.

Burth, S., Kraus, T. and Wohlwend, H., 2001. The pricing of structured products in the Swissmarket. Journal of Derivatives 9 (Winter), 30--40.

Finnerty, J., 1993. Interpreting SIGNs. Financial Management Summer, 34--47.

Grünbichler, A. and Wohlwend, H., 2004. The valuation of structured products: Empirical findingsfor the Swiss market. 7th Conference of the Swiss Society for Financial Market Research.Zürich, Switzerland.

Hull, John, 2003. Options, Futures, and Other Derivatives, Fifth Edition, Pearson Education, Inc.Upper Saddle River, New Jersey.

Mason, S., 1995. Contingent Claim Analysis, in: Mason, S., Merton, R, Perold, A., and Tufano, P.,Cases in Financial Engineering: Applied Studies of Financial Innovation, Prentice Hall, Inc.Englewood Cliffs, New Jersey.

National Association of Securities Dealer. Notice to Members 05-59 Guidance Concerning the Saleof Structured Products (September 2005).

Stoimenov, P., and Wilkens, S., 2005. Are structured products ‘fairly’ priced? An analysis of theGerman market for equity-linked instruments. Journal of Banking and Finance 29, 2971--2993.

Szymanowska, M., Horst, J, and Veld, C., 2004. An empirical analysis of pricing Dutch reverseconvertible bonds, 2004 FMA Annual Meeting.

Wilkens, S., Erner, C., and Roder, K., 2003. The pricing of structured products in german market. Journal of Derivatives 11 (Fall), 55--69.

Wilkens, S., and Roder, K., 2003. Reverse convertibles and discount certificates in the case of constant and stochastic volatilities. Financial Markets and Portfolio Management 17, 76--102.

Wilkens, S., and Stoimenov, P., 2006. The pricing of leverage products: An empirical investigationof the German market for ‘long’ and ‘short’ stock index certificates. Journal of Banking and Finance Forthcoming.



28

TABLE 1

Descriptive statistics for the reverse exchangeable bond markets. The statistics include the meavalues of 1) the issue size measured in millions of $, 2) the term to maturity in number of calendin level as a percentage of the strike price, 4) knock-out level as a percentage of the strike price6) the strike price as a percentage of the underlying asset price at the time of the issue, 7) the selcertificate (issue price) as a percentage of the underlying asset price at the time of the issue, 8) t

value of the markets, and 9) the total number of issues of bonds.

Total Number of Issues

Total Amount Issued($ Mill.) a

/ Reported Cases (%)Issue Size($ Mill.) b

Maturity(# of days) KI (%) c KO (%) c

CouponRate

Plain Vanilla

Mean 665 6,704 10.08 304 n.a. n.a. 10.81

Median(95.54%)

5.00 365 n.a. n.a. 10.00

Discount Certificates

Mean 2,016 9,915 4.92 135 n.a. n.a. 0.00

Median(92.06%)

5.00 49 n.a. n.a. 0.00

Knock-In

Mean 4,662 27,965 6.00 257 76.79 n.a. 12.14

Median(88.27%)

3.00 359 80.00 n.a. 11.50

Knock-Out

Mean 83 409 4.93 278 n.a. 120.08 9.27

Median(75.90%)

2.00 362 n.a. 120.00 10.88

Total

Mean 7,426 45,156 6.08 228 76.79 120.08 8.69

Median(89.90%)

3.50 185 80.00 120.00 9.75

a estimated total amount issued in million dollars based on a percentage of the cases with reported issue size b in million dollarslevel as a percentage of the strike price d as a percentage of the underlying asset’s price on the issue date



29

TABLE 2

Descriptive statistics for the reverse exchangeable bonds market by issue year and type. The statistics inamount issued in million dollars, 2) the number of issues, and 3) the percentage of issues per type per ye

Plain Vanilla Discount Certificates Knock-In Knock-Out

Year Amount a Issues % Amount a Issues % Amount a Issues % Amount a Issues %

1998 195 3 60.0 4 2 40.0 n.a. n.a. n.a. n.a. n.a. n.a.

1999 504 15 21.4 939 48 68.6 129 7 10.0 n.a. n.a. n.a.

2000 709 41 23.2 1,012 92 52.0 226 23 13.0 41.53 21 11.9

2001 1,346 55 26.4 1,751 130 62.5 156 21 10.1 2.99 2 1.0

2002 377 30 10.3 1,489 246 84.3 82 16 5.5 n.a. n.a. n.a.

2003 1,147 66 13.6 1,809 371 76.3 615 48 9.9 n.a. 1 0.2

2004 837 103 16.3 1,226 249 39.3 2,016 279 44.1 6 2 0.3

2005 611 117 9.4 939 289 23.3 5,849 824 66.4 39 11 0.9

2006 1,053 203 5.7 1,493 503 14.2 15,851 2,797 79.1 208 34 1.0

2007b 38 34 4.4 239 86 11.1 2,899 645 83.0 55 12 1.5

Total 6,704 665 9.0 9,915 2,016 27.2 27,965 4,662 62.8 409 83 1.1

a estimated total amount issued in million dollars based on a percentage of the cases with reported issue size b bonds issued on or before Feb



30

TABLE 3

Total dollar amount (in millions of US Dollars) and number of issues of reverseexchangeable bonds by year and by country in which the issuing banks are located and inwhich more than 100 bonds were issued. The data covers from 1998 to February 2007.

Panel A: Total Dollar Amounta

Switzerland Germany Great Britain Luxembourg Netherlands United States Total

1998 n.a. 4 165 n.a. n.a. n.a. 199

1999 242 49 1,458 98 10 n.a. 1,715

2000 381 276 1,450 122 117 n.a. 2,246

2001 263 682 2,443 64 281 112 3,410

2002 114 215 1,361 15 720 32 1,979

2003 74 466 935 29 1,936 203 3,557

2004 40 78 1,947 200 1,349 408 4,066

2005 5 1,428 3,192 177 1,730 832 7,404

2006 45 4,367 6,159 431 4,451 3,461 18,526

2007b 84 848 671 17 706 441 3,159

Total 1,253 7,529 17,875 1,128 11,330 5,608 45,156

Panel B: Issues

Switzerland Germany Great Britain Luxembourg Netherlands United States Total

1998 n.a. 2 2 n.a. n.a. n.a. 5

1999 5 8 46 7 1 n.a. 70

2000 21 34 96 11 13 n.a. 177

2001 16 63 95 15 10 8 208

2002 7 30 66 3 176 8 292

2003 5 55 53 7 342 20 486

2004 3 18 145 55 307 88 633

2005 8 192 339 39 466 183 1,241

2006 24 425 882 51 1,362 646 3,537

2007b 28 52 182 6 253 164 777

Total 117 879 1,906 194 2,931 1,117 7,426a Estimated total dollar amount in millions of US Dollars based on a percentage of the cases with reported issue size b bondsissued as of February 20, 2007



31

TABLE 4

The number of issues, average term to maturity (in years), standard deviation of the underlying asset dividend yield, and profitability measured by the profit (∏) as a percentage of the total issuing cost foexchangeable bonds. The p-value tests the probability that the profitability is equal to zero.

Type StatisticTotal Number

of IssuesMaturity(Years) Volatility

EquivalentDividend Yield

ProfitPerc

Plain Vanilla

Mean 580 0.87 37.53 1.74

Median 1.00 34.76 0.93


Mean 1,922 0.35 41.93 1.14

Median 0.13 38.10 0.00

Knock-InMean 3,944 0.71 40.24 1.49

Median 1.00 39.31 0.56

Knock-Out

Mean 69 0.77 48.84 1.46

Median 1.00 42.96 0.30

Total

Mean 6,515 0.62 40.59 1.41

Median 0.51 38.61 0.16



32

TABLE 5

The number of issues, average term to maturity (in years), standard deviation of the underlying assedividend yield, and profitability measured by the profit (∏) as a percentage of the total issuing costexchangeable bonds by issue year. The p-value tests the probability that the profitability is equal to

Panel A: By Issue Year

Issue Year StatisticTotal Number of

Issues Maturity (Years) VolatilityEquivalent

Dividend Yield Profitability in Pe

1998

Mean 5 1.59 36.82 1.73 3.80

Median 1.03 37.77 1.40 2.16

1999

Mean 68 1.02 49.63 1.21 6.69

Median 1.00 44.54 0.39 5.19

2000

Mean 171 0.95 60.97 1.03 7.55

Median 1.01 56.63 0.16 6.03

2001

Mean 197 0.95 61.92 0.85 9.12

Median 1.00 59.07 0.23 6.23

2002

Mean 288 0.55 50.53 1.17 3.48

Median 0.24 48.62 0.00 1.43

2003

Mean 469 0.46 40.91 1.03 3.35

Median 0.17 37.52 0.00 0.97

2004

Mean 606 0.67 37.58 1.43 4.70

Median 0.97 35.37 0.00 2.79

2005

Mean 1,135 0.69 35.87 1.67 4.87

Median 0.99 34.67 0.67 3.74

2006

Mean 2,964 0.58 39.66 1.55 4.59

Median 0.50 39.10 0.18 3.77

2007a

Mean 612 0.52 38.39 0.97 3.98

Median 0.48 37.60 0.00 3.29a bonds issued on or before February 20, 2007



33

TABLE 6

The number of issues, average term to maturity (in years), standard deviation of the underlying assedividend yield, and profitability measured by the profit (∏) as a percentage of the total issuing costexchangeable bonds by maturity and country of the issuing bank. The p-value tests the probability

equal to zero.Panel A: By Maturity

Maturity StatisticTotal Number of


Dividend Yield Profitability in Pe

T ≤ 1

Mean 5,095 0.48 40.54 1.41 4.16

Median 0.27 39.05 0.00 3.07

1 < T ≤ 2

Mean 1,363 1.06 41.12 1.38 6.33

Median 1.02 37.08 0.78 4.89

T > 2

Mean 61 2.47 32.85 2.41 12.59

Median 2.04 31.27 2.18 5.20

Panel B: By Country of the Issuing Bank

CountryTotal Number of


Dividend YieldProfitability in

Percentage

Switzerland 95 0.77 45.67 1.42 5.50

Germany 822 0.62 41.95 1.57 4.75

Great Britain 1,635 0.85 40.33 1.46 5.74

Luxembourg 181 0.81 39.32 1.69 5.03

Netherlands 2,719 0.36 39.43 1.46

United States 864 0.90 43.43 0.98 7.61



34

TABLE 7

In Panel A we compare the market capitalization for all 826 underlying securitieswith the average market capitalization for all the firms in the same industry at thecountry level as well as the regional level. We also calculate the average ranking

in market capitalization of underlying assets against all the firms in the sameindustry at the country level as well as at the regional level. In Panel B wecompare the dividend yield for all 826 underlying securities with the averagedividend yield for all the firms in the same industry at the country level as well asthe regional level. We also calculate the average ranking in dividend yield of underlying assets against all the firms in the same industry at the country level aswell as at the regional level. Based on the underlying securities’ characteristics asof April 25, 2007.

Underlying Asset Country Region

Panel A

Market Capitalization (€ Million) 26,130.37 9,135.23 6,494.91

p-value a < 0.001 < 0.001

Percentile Ranking b 84.4 87.1

p-value c < 0.001 < 0.001

Panel B

Average Dividend Yield (%) 2.23 1.29 1.21

p-valued

< 0.001 < 0.001

Percentile Ranking b 74.8 74.9

p-value c < 0.001 < 0.001

a The probability that the average difference between the underlying asset’s market capitalization and theaverage market capitalization for all the firms in the same industry to be zero. b The formula used to compute the percentile ranking is the following:

Percentile Ranking =

⎥

⎥⎥⎥

⎦

⎤

⎢

⎢⎢⎢

⎣

⎡ −+

+−

2

Rank Absolute1Rank Absolute

N

N

N

N

c The probability that the percentile ranking is indifferent from 50%.d The probability that the average difference between the underlying asset’s dividend yield and the averagedividend yield for all the firms in the same industry to be zero.





36

TABLE 9

Realized return for the expired cases by type. The statistics include themean, the median, and number of observations of 1) the annualized priceappreciation, and 2) the annualized total return for the certificates,

underlying security, and the index comprehensive of the market of theunderlying security.

Security Type

Annualized Total Return

Statistic REX Underlying Index

Plain Vanilla

Mean 1.75 15.40 a 8.40 b,c

St. Dev. 18.08 59.40 22.29

n 538


Mean -0.19 45.76 a 9.62 b,c

St. Dev. 29.24 290.07 42.97

n 1,904

Knock-In

Mean 5.46 29.93 a 13.45 b,c

St. Dev. 19.90 83.53 20.94

n 2,692

Knock-Out

Mean -6.44 1.42 1.56

St. Dev. 27.99 76.88 16.40

n 60

Total

Mean 2.87 33.90 a 11.38 b,c

St. Dev. 23.86 188.39 31.28

n 5,194

a the average difference of the underlying asset’s return and the bond’s return is equal to zero andsignificant at the 0.01 level b the average difference of the index’s return and the bond’s return isequal to zero and significant at the 0.01 level c the average difference of the index’s return and theunderlying asset’s return is equal to zero and significant at the 0.01 level



37

Appendix 1: Example of a Plain Vanilla Reverse Exchangeable

Bond

ABN AMRO Bank N.V.

MEDIUM-TERM NOTES, SERIES A

Senior Fixed Rate Notes10.50% Reverse ExchangeableSM

Securities due August 18, 2005

linked to common stock of Motorola, Inc.

Securities: 10.50% Reverse Exchangeable Securities due August 18, 2005.

Underlying Shares: Common stock, par value $3.00 per share of Motorola, Inc.

Interest Rate:10.50% per annum, payable semi-annually in arrears on February 18, 2005 andAugust 18, 2005.

Issue Price: 100%

Issue (Settlement) Date: August 18, 2004

Maturity Date: August 18, 2005

Initial Price: $14.21

Stock Redemption

Amount:

70.37 Underlying Shares for each $1,000 principal amount of the Securities, whichis equal to $1,000 divided by the initial price.

Determination Date: The third trading day prior to the maturity date.

Payment at maturity:The payment at maturity is based on the closing price of the Underlying Shares onthe determination date.

•

If the closing price per Underlying Share on the determination date is at or above the initial price, we will pay the principal amount of each Security incash.

• If the closing price per Underlying Share on the determination date is below theinitial price, we will deliver to you, in exchange for each $1,000 principalamount of the Securities, a number of Underlying Shares equal to the stock redemption amount. You will receive cash in lieu of fractional shares.

No Affiliation with

Motorola, Inc.:

Motorola, Inc., which we refer to as Motorola, is not an affiliate of ours and is notinvolved with this offering in any way. The obligations represented by the Securitiesare our obligations, not those of Motorola. Investing in the Securities is notequivalent to investing in Motorola common stock.

Listing: We do not intend to list the Securities on any securities exchange.



38

Appendix 2: Example of a Knock-In Reverse Exchangeable Bond

ABN AMRO Bank N.V.MEDIUM-TERM NOTES, SERIES A

Senior Fixed Rate Notes

10.50% Knock-In Reverse Exchangeable

SM

Securities due August 18, 2005linked to common stock of Circuit City Stores, Inc.

Securities: 10.00% Knock-in Reverse Exchangeable Securities due August 18, 2005.

Underlying Shares: Common stock, par value $0.50 per share of Circuit City Stores, Inc.

Interest Rate:10.00% per annum, payable semi-annually in arrears on February 18, 2005 andAugust 18, 2005.

Issue Price: 100%

Issue (Settlement) Date: August 18, 2004

Maturity Date: August 18, 2005

Initial Price: $12.36

Knock-in Level: $8.65, which is 70% of the initial price.

Stock Redemption

Amount:

80.90 Underlying Shares for each $1,000 principal amount of the Securities, which isequal to $1,000 divided by the initial price.

Determination Date: The third trading day prior to the maturity date.

Payment at maturity: The payment at maturity is based on the performance of the Underlying Shares on thedetermination date.

• If the market price of the Underlying Shares on the primary U.S. exchange or market for the Underlying Shares has not fallen to or below the knock-in level onany trading day from but not including the trade date to and including thedetermination date, we will pay you the principal amount of each Security incash.

• If the market price of the Underlying Shares on the primary U.S. exchange or market for the Underlying Shares falls to or below the knockin level on anytrading day from but not including the trade date to and including thedetermination date:

— we will deliver to you a number of Underlying Shares equal to the stock redemption amount, in the event that the closing price of the UnderlyingShares on the determination date is below the initial price; or

— we will pay you the principal amount of each Security in cash, in the event

that the closing price of the Underlying Shares on the determination date is ator above the initial price.

• You will receive cash in lieu of fractional shares.

No Affiliation with

Circuit City Stores, Inc.:

Circuit City Stores, Inc., which we refer to as Circuit City, is not an affiliate of oursand is not involved with this offering in any way. The obligations represented by theSecurities are our obligations, not those of Circuit City. Investing in the Securities isnot equivalent to investing in Circuit City common stock.

Listing: We do not intend to list the Securities on any securities exchange.



39

Appendix 3: Distribution of Issues Classified by Two-Digit SIC Codes of Underlying Securities

2- Digit SIC Industry Obs. Frequency

Mining

10 Metal Mining 374

12 Coal Mining 8513 Oil and Gas Extraction 563

Others 33 1,055 14.21%

Construction

15 Building Construction-General Contractors and Operative Builders 37 37 0.50%

Manufacturing

20 Food and Kindred Products 58

21 Tobacco Products 89

26 Paper and Allied Products 35

28 Chemicals and Allied Products 526

29 Petroleum Refining and Related Industries 187

30 Rubber and Miscellaneous Plastics Products 31

32 Stone, Clay, Glass, and Concrete Products 6733 Primary Metal Industries 406

35 Industrial and Commercial Machinery and Computer Equipment 1,017

36 Electronic and Other Electrical Equipment and Components 1,244

37 Transportation Equipment 144

38 Measuring, Analyzing, and Controlling Instruments 56

Others 71 3,931 52.94%

Transp., Communications, Electric, Gas, and Sanitary Serv.

45 Transportation by Air 111

48 Communications 179

49 Electric, Gas, and Sanitary Services 42

Others 32 364 4.90%

Wholesale Trade and Retail Trade53 General Merchandise Stores 112

54 Food Stores 30

56 Apparel and Accessory Stores 56

58 Eating and Drinking Places 59

59 Miscellaneous Retail 30

Others 92 379 5.10%

Finance, Insurance, and Real Estate

60 Depository Institutions 525

62 Sec. and Commodity Brokers, Dealers, Exchanges, and Services 159

63 Insurance Carriers 93

67 Holding And Other Investment Offices 253

Others 46 1,076 14.49%

Services

70 Hotels, Rooming Houses, Camps, and Other Lodging Places 40

73 Business Services 484

78 Motion Pictures 30

Others 30 584 7.86%

Total 7,426 100.00%



40

Appendix 4

In this Appendix, we will show that the payoff of a plain vanilla reverse exchangeable bond

is the same as the combined payoffs of the following three positions:

1. A long position in one zero coupon bond with face value equal to $1,000 and maturity

date same as the maturity date of the reverse exchangeable;

2. A long position in zero coupon bonds of which the face values equal the coupons

payments of the reverse exchangeable and maturity dates are the reverse

exchangeable coupon payment dates;

3. A short position in put options with exercise price of I0, term to expiration of T

(which is the term to maturity of the reverse exchangeable), and number of options of

0I

000,1$.

The redemption value, from Equation (1), for holding one plain vanilla reverse exchangeable

bond, VT, is:

⎪⎩

⎪⎨⎧

<

≥=

0T

0

T

0T

T II if I

$1,000I

II if $1,000V

⎥⎦

⎤⎢⎣

⎡=

0I

I$1,000$1,000,Min T

⎥⎦

⎤⎢⎣

⎡=

0I

I1,Min$1,000 T

⎥⎦

⎤

⎢⎣

⎡

−+= 1I

I

0,Min$1,000$1,0000

T

[ ]0

0

II0,MinI

$1,000 +$1,000= −T …(A4-1)



41

The [ ]0II,0Min −T in Equation (A4-1) is the payoff for a short position for a put option with

an exercise price of I0. The negative value of VT is

]I-I[0,MinI

000,1$

-$1,000-V- 0T0

T=

]I-I[0,MaxI

000,1$ $1,000- T0

0

+= …(A4-2)

The [ ]T II,0Max 0 − in Equation (A4-2) is the payoff for a long position in a put with an

exercise price of I0.

The long positions in the zero coupon bonds will generate the payoff $1,000 on maturity date

T plus the coupons on the coupon payment dates. The payoff $1,000 in Equation (A4-1) can be

duplicated by taking a long position in a zero coupon bond with the face value equal to $1,000

and maturity T. The payoff [ ]0T II,0Min − in Equation (A4-1) is the payoff of a short position

for a put on the underlying asset with an exercise price I 0. So the payoff for investing in one

plain vanilla reverse exchangeable bond is the same as the three positions given at the beginning

of the Appendix.



42

Appendix 5

In this Appendix, we will show that the payoff of a discount certificate is the same as the

combined payoffs of the following two positions:

1. A long position in one zero coupon bond with face value equal to the exercise price,

X and maturity date same as the maturity date of the discount certificate;

2. A short position in put options with exercise price of X, term to expiration of T

(which is the term to maturity of the discount certificate), and a number of options

equal to one.

The redemption value for holding one discount certificate, VT at t=T, can be expressed as:

⎩⎨⎧

<

≥=

X

X T

TT

T

I if I

XI if V

[ ]IX,Min T=

[ ] X T −I0,Min+X= …(A5-1)

The [ ] X I T −,0Min in Equation (A5-1) is the payoff for a short position in a put with an

exercise price of X. The negative value of VT is

X]-I[0,Min--V- TT X =

]I-X[0,Max- T+= X …(A5-2)

The [ ]T I X −,0Max in Equation (A5-2) is the payoff for a long position in a put with an

exercise price of X.

Comparing Equation (A5-2) to Equation (A4-2), we find that they are different only by a

scale of 0

000,1$

I when X = I0, which is the number of contracts of the put option. Based on the

results, we can conclude that a discount certificate is a special case of a plain vanilla reverse



43

exchangeable bond when a plain vanilla reverse exchangeable bond is a zero coupon bond and

when the number of contracts of the embedded put options is one.

The payoff $1,000 in Equation (A5-1) can be duplicated by taking a long position in a zero

coupon bond with the face value equal to X and maturity T. The payoff [ ] X T −I0,Min in

Equation (A5-1) is the payoff of a short position for a put on the underlying asset with an

exercise price X. So the payoff for investing in one discount certificate is the same as the two

positions given at the beginning of the Appendix.



Appendix 6

In this Appendix, we present the approach we use calculating the equivalent continuous

dividend yield for stocks that pay discrete dividends. For an underlying asset which is an

individual stock with a price I0 at t=0 (the issue date) and which pays n dividends during a time

period T with cash dividend Di being paid at time ti, the equivalent dividend yield q will be such

that

T qt r n

i i eSe DS i 0

10

' −−

==− ∑

0

1

0

10

''

1 S

e D

S

e DS

e

ii t r n

i it r n

i iT q

−

=

−

=− ∑∑−=

−

=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−=−

−

=∑0

1

'

1lnS

e DqT

it r n

i i

T

S

e D

q

it r

i i

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−

−=

−

=∑0

4

1

'

1ln

Documents

Reverse Exchangeable Securities